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Soon after Rubio began speaking at the Kemp Forum on Expanding Opportunity, five separate, small groups of protesters stood up to interrupt the Florida senator

The protests marked the first time Rubio has been interrupted in such a fashion on the campaign trail

Columbia, South Carolina (CNN)Sen. Marco Rubio was repeatedly heckled over his immigration platform Saturday while speaking here at a forum on poverty, with protesters suggesting that the Cuban-American senator does not represent the Hispanic community.

Soon after Rubio began speaking at the Kemp Forum on Expanding Opportunity, five separate, small groups of protesters stood up to interrupt the Florida senator, shouting chants such as "undocumented and unafraid."

"Rubio does not represent the Hispanic community. He wants to deport our families," one person yelled as security led him out. Two other protesters held up signs that read, "Rubio wants to deport me!"

The protests marked the first time Rubio has been interrupted in such a fashion on the campaign trail. None of the other candidates who appeared at the forum -- including Ohio Gov. John Kasich, former Florida Gov. Jeb Bush, former Arkansas Gov. Mike Huckabee, retired neurosurgeon Ben Carson and New Jersey Gov. Chris Christie -- were interrupted.

Rubio, appearing onstage with Kasich, House Speaker Paul Ryan and South Carolina Sen. Tim Scott, kept calm as security removed the protesters. But the Florida senator refused to back down on the issue.

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"We're going to enforce our immigration laws, guys," he said, to huge applause from the Republican audience, which had packed a convention center's auditorium to standing room-only.

As the protesters Saturdaycontinued to stand up and shout, the candidates were forced to acknowledge them.

Kasich noted that the protesters had a right to speak, and, along with Rubio, took a thinly-veiled swipe at GOP front-runner Donald Trump, whose rallies are consistently the target of protesters.

"I thought about handling them the way another candidate does, but I thought I'd wait. It's not my ..." Rubio trailed off, to applause.

"I saw a crowd booing this woman who was being escorted. That's not the spirit of Jack Kemp. I mean, we are people that can tolerate differences," the Ohio governor said.

In contrast, audience members at Saturday's event didn't boo or heckle the protesters as they left the auditorium.

Eventually, however, Kasich grew tired of the interruptions.

"If there any more protesters out there, I think we got the point. If you keep disrupting, you're just going to turn everyone against you, so we heard you," Kasich said.

"Can you yell when John speaks?" Rubio joked.

The Rubio campaign said it had nothing to add to Rubio's response. Columbia police Sgt. Paul Blendowski told CNN the protesters left the forum "on their own accord" and no arrests were made.

"At the request of event property management, anyone who causes a disturbance is asked to leave," Blendowski said.

Later Saturday, United We Dream, an advocacy organization focused on immigrant youth that fights against deportations and family separation, put out a statement highlighting the protests, accusing Rubio of "turning his back" on immigrants despite playing up his family's immigrant story on the trail. Rubio's parents came to the U.S. from Cuba.

"This morning, I confronted Marco Rubio on his anti-immigrant, anti-DACA rhetoric that seeks to take away the program that allows me to work, pursue my dreams, and be protected from deportation. He has turned his back on the immigrant community and we will continue to stand up to his attacks," said Deya Aldana, who is from New Jersey, in the statement.

Aldana was referring to Deferred Action for Childhood Arrivals, a policy that protects some undocumented immigrants who came to the U.S. as children from deportation. Rubio has increasingly opposed the policy, which he criticizes as an illegitimate executive action.

Rubio is often seen as one of the more moderate GOP candidates on immigration, having been an author of the bipartisan immigration reform bill that passed the Senate but died in the House in 2013.

Since then, however, Rubio has moved away from that bill, which would have created a pathway to citizenship for undocumented immigrants living in the U.S., and has faced criticism for being soft on immigration from his fellow 2016 candidates.